EP2963883B1 - Method for blind phase tracking for fbmc receiver - Google Patents

Description

TECHNICAL AREA

The present invention generally relates to the field of telecommunications systems using a multi-carrier filterbank modulation, also called Filter Bank Multi-Carrier (FBMC) systems. The present invention more particularly relates to a blind phase tracking method in a FBMC receiver.

STATE OF THE PRIOR ART

Telecommunication systems using a multi-carrier modulation are well known in the state of the art. The principle of such a modulation consists in dividing the transmission band into a plurality of sub-channels associated with sub-carriers and modulating each of these sub-carriers by the data to be transmitted.

The most widespread multi-carrier modulation is undoubtedly Orthogonal Frequency Division Multiplexing (OFDM) modulation. This is implemented in WLAN wireless LANs, WiFi, high-speed wireless Internet access (WiMAX), digital broadcasting systems (DVB-T, ISDB-T, DAB), links asymmetric digital (xDSL), fourth generation cellular telephony (LTE), etc.

In an OFDM transmission system, each OFDM symbol block is preceded by a guard interval or a cyclic prefix, which is longer than the temporal spread of the impulse response of the channel, so as to eliminate the interference intersymbol. Inserting a guard interval or a prefix, however, leads to a loss of spectral efficiency. Finally, since the spectral occupation of an OFDM signal is substantially greater than the subcarrier band that it uses due to the spread of the side lobes, the OFDM modulation is not an optimal solution for applications requiring high out-of-band rejection rates.

FBMC ( Filter Bank Multi Carrier ) modulation can be used as an alternative to OFDM modulation.

A comparison between FBMC systems and OFDM systems is presented in the article by B. Farhang-Bouroujeny entitled "OFDM versus filter bank multicarrier" published in IEEE Signal Processing Magazine, pp. 91-112, March 2011 .

The principle of FBMC modulation is based on a filter bank synthesis on transmission and a filter bank analysis on reception.

The Fig. 1 schematically shows the structure of a first transmission / reception system FBMC known from the state of the art.

This structure has been described in detail in the article by B. Hirosaki titled "An orthogonally multiplexed QAM system using the discrete Fourier transform" published in IEEE Trans on Comm., Vol. 29 No. 7, pp. 982-989, July 1981 , as well as in the article of P. Siohan et al. entitled "Analysis and design of OFDM / OQAM systems based on filterbank theory" published in IEEE Trans .on signal processing, Vol 50, No 5, pp. 1170-1183, May 2002 .

At the transmitter, the QAM modulation symbols to be transmitted with a rate Nf where f = 1 / T are grouped in blocks of size N, x ₀ [ m ], ..., x _{N -1} [ m ], where m is the time index of the block. Each block of N symbols is provided in parallel with N input channels of a preprocessing module 110, called preprocessing OQAM (Offset QAM). This preprocessing module performs a modulation of the OQAM type data, that is to say, temporally demultiplexes the real part and the imaginary part of x _k [ m ] with a rate of 2 f .

The samples thus obtained are provided in the form of blocks of size N to a synthesis filterbank 120, consisting of an IFFT module (inverse fast Fourier transform) of size N, 130, of a plurality N of polyphase filters. 133, of a plurality of oversamplers 135, of factor M = N / 2, at the output of the different polyphase filters, and finally of a plurality of delays, 137, arranged in parallel and varying from 0 to N - 1 periods sampling. Each of the N treatment channels corresponds to a subchannel.

The outputs of the polyphase, oversampled and delayed filters are summed by the adder 139 before translation at an RF frequency (not shown) and transmission on the channel 150.

The polyphase filters are frequency-translation versions of k / MT of a prototype filter whose impulse response is of LT duration, ie the output of a polyphase filter temporally overlaps the output of the adjacent polyphase filter of M samples. It follows that a polyphase filter output temporally overlaps The other outputs of polyphase filters. The coefficient L is called for this reason overlapping factor .

On the receiver side, after baseband demodulation, the received signal is sampled at a rate Nf. The samples are provided as N- sized blocks to an analysis filterbank 160, including a plurality of delays 163 arranged in parallel and ranging from 0 to N -1 sampling periods in the order inverse delays 137. The flow of samples from different delays are then decimated by a factor M = N / 2 by the decimators 165 and filtered by the analysis filters 167. The analysis filters have a combined impulse response and reversed temporally with respect to the corresponding synthesis filter. Since the prototype filter is real-valued, and symmetrical by time inversion, it can be shown that an analysis filter has the same impulse response as the corresponding synthesis filter. Combining a synthesis filter with the corresponding analysis filter (produces transfer functions) gives a Nyquist filter.

The symbols at the output of the synthesis filters are then subject to an FFT (Fast Fourier Transform) of size N at 170, the different frequency components of the FFT being then supplied to the post-processing module 180 performing a reverse processing of that of pretreatment 110.

The synthesis / analysis filtering being carried out in the time domain, respectively at the output of the IFFT module and at the input of the FFT module, the FBMC system illustrated in FIG. Fig. 1 will be said implemented in the time domain.

The FBMC system is also likely to be implemented in the frequency domain as described in the M. Bellanger et al. entitled "FBMC physical layer: a primer" available at www.ict-phydyas.org . In this case, the synthesis filtering is performed in the frequency domain upstream of the IFFT module and, similarly, the analysis filtering is performed in the frequency domain upstream of the FFT module.

Whatever the type of implementation, one of the main problems to be solved is to estimate and correct the phase terms that may affect the symbols of the different sub-carriers (at the output of the FFT module for a time implementation and output of the filters analysis for a frequency implementation). These phase terms can come from different origins.

Firstly, they may be due to an imperfect synchronization between the transmitter and the receiver, more precisely between the oscillator of the transmitter ensuring the translation in RF band and the oscillator of the receiver ensuring the reverse translation in band of base of the received signal. Imperfect synchronization here means a frequency difference or CFO ( Carrier Frequency Offset ). Even when receiver frequency estimation and correction is predicted, this correction is generally insufficient due to bias of the estimator and a phase residual may be present.

Then, these phase terms can be due to a phase drift and / or frequency of the receiver oscillator. This phase / frequency drift can be attributable in particular to aging, to temperature variations, or to intrinsic instability of the oscillators. In this case, it is not possible to synchronize the oscillators and phase compensation must be performed as the reception progresses.

Finally, these phase terms may be due to variations in the characteristics of the propagation channel (Doppler shift for example). Indeed, when the channel estimate does not allow a sufficiently fast equalization, uncompensated phase terms can appear at the receiver.

Different phase tracking techniques are known from the state of the technical. Diagrammatically, supervised techniques, blind techniques and hybrid techniques can be distinguished. The supervised techniques make use of pilot symbols distributed in a predetermined manner within the stream of symbols to be transmitted. With these pilot symbols, a measurement of the phase can be performed reliably and periodically. The so-called blind techniques, on the other hand, assume no prior knowledge of the transmitted symbols but resort to either statistical properties of the signal or to a rough first estimation of the received symbols ( decision directed estimation ). Finally, hybrid techniques successively implement supervised estimates and blind estimates. For example, when the data is transmitted as packets having a preamble and a payload, it is known to incorporate pilot symbols into the preamble to allow supervised estimation at the beginning of the packet. This estimate can then continue blindly upon receipt of the payload.

Supervised estimation techniques have been widely explored in the context of OFDM modulation. Examples of this can be found in the article of M. Speth et al. entitled "Optimum receiver design for OFDM-based broadband transmission-Part II": a case study "published in IEEE Trans. on Comm., Vol. 49, No. 4, April 2011, pages 571-578 .

lorsque le symbole x_k (m) est transmis sur la partie réelle et : $$s_k\left(n\right)={\epsilon }_k\left(n\right)+{\mathit{jx}}_k\left(n\right)$$

où ε _k (n) est un terme d'interférence dépendant des données sur les sous-porteuses adjacentes et en des instants adjacents ainsi que de la réponse du filtre prototype.These estimation techniques are however not easily transferable to the FBMC receivers because of the specificities of the OQAM modulation. Indeed, even assuming that the FBMC receiver is perfectly synchronized with the transmitter and in the absence of noise, a complex symbol obtained at the output of the FFT module, at time m and on the subcarrier k , can be expressed Under the form : $$s_k\left(m\right)=x_k\left(m\right)+{\mathit{j\epsilon }}_k\left(m\right)$$

when the symbol x _k ( m ) is transmitted on the real part and: $$s_k\left(\mathrm{not}\right)={\epsilon }_k\left(\mathrm{not}\right)+{\mathit{jx}}_k\left(\mathrm{not}\right)$$

where ε _k ( n ) is an interfering term dependent on the subcarrier data adjacent and in adjacent moments as well as the response of the prototype filter.

où x_k (m) est le symbole réel porté par la sous-porteuse k, n_k (m) est un échantillon de bruit sur la porteuse k, à l'instant m et φ(m) est le déphasage en cet instant.If one takes the case of a data transmitted on the real part and if one supposes that the symbol received is affected by a term of phase, this one can express itself in the form: $$r_k\left(m\right)=\left(x_k\left(m\right)+{\mathit{j\epsilon }}_k\left(m\right)\right)\exp \left(\mathit{j\phi }\left(m\right)\right)+{\mathrm{not}}_k\left(m\right)$$

where x _k ( m ) is the actual symbol carried by the subcarrier k, n _k ( m ) is a noise sample on the carrier k, at time m and φ ( m ) is the phase shift at this instant.

où x̂_k (m) est le symbole (réel) estimé par le récepteur pour l'instant m et la sous-porteuse k. Autrement dit : $$\hat{\phi }\left(m\right)=\arg \left({\displaystyle \sum _{k=0}^{K-1}}{\left|x_k\left(m\right)\right|}^2\exp \left(\mathit{j\phi }\right)+{\mathit{jI}}_k\left(m,\phi \right)+N_k\left(m\right)\right)$$

avec I_k (m,φ) = ε _k (m)x_k (m)exp(jφ) et N_k (m) = x_k (m)n_k (m). Si le nombre de termes sous le signe somme est suffisamment important (grand nombre de porteuses), la somme des termes I_k (m,φ) tend à s'annuler en moyenne, et l'estimateur présente de bonnes performances. En pratique toutefois, le terme d'interférence I_k (n,φ) peut être localement très grand devant |x_k (n)|², ce qui conduit à des estimations de phase erronées et un taux d'erreurs symbole élevé.A blind phase tracking method for a FBMC receptor has been proposed in the article of P. Amini et al. titled "Packet format design and decision directed tracking methods for multicarrier systems bank" published in EURASIP Journal on Advances in Signal Processing, 2010 . This method uses a partial information of each symbol by estimating the phase shift by means of: $$\hat{\phi }\left(m\right)=\arg \left({\displaystyle \underset{k=0}{\overset{K-1}{\Sigma }}}{r}_k\left(m\right){\hat{x}}_k\left(m\right)\right)$$

where x _k ( m ) is the (real) symbol estimated by the receiver for the moment m and the subcarrier k . In other words : $$\hat{\phi }\left(m\right)=\arg \left({\displaystyle \underset{k=0}{\overset{K-1}{\Sigma }}}{\left|x_{\mathrm{<figure-callout\; id="2"\; label="k\; m"\; filenames="imgf0001.png,imgf0008.png"\; state="\{\{state\}\}">k\; </figure-callout>}}\left(m\right)\left(\right)\right|}^2\exp \left(\mathit{j\phi }\right)+{\mathit{jI}}_k\left(m,\phi \right)+{\mathrm{NOT}}_k\left(m\right)\right)$$

with I _k ( m , φ ) = ε _k ( m ) x _k ( m ) exp ( j φ) and N _k ( m ) = x _k ( m ) n _k ( m ). If the number of terms under the sign sum is large enough (large number of carriers), the sum of the terms I _k ( m , φ ) tends to cancel out on average, and the estimator has good performances. In practice, however, the interference term I _k ( n , φ) can be locally very large before | x _k ( n ) | ² , which leads to erroneous phase estimates and a high symbol error rate.

The object of the present invention is to propose a method of tracking blind or hybrid phase in a FBMC receiver, which does not have the drawbacks of the state of the art, in particular that makes it possible to substantially reduce the symbol error rate while being particularly simple and robust.

STATEMENT OF THE INVENTION

The present invention is defined by a blind phase tracking method for FBMC receiver as given by claim 1. Advantageous embodiments are given in the dependent claims.

BRIEF DESCRIPTION OF THE DRAWINGS

• La Fig. 1 représente un système de télécommunication FBMC connu de l'état de la technique ;
• La Fig. 2 représente un récepteur FBMC utilisant une méthode de poursuite de phase selon un mode général de réalisation de l'invention ;
• La Fig. 3A représente un module d'estimation de phase permettant de mettre en oeuvre une poursuite de phase selon un premier mode de réalisation de l'invention ;
• La Fig. 3B représente un module d'estimation de phase permettant de mettre en oeuvre une poursuite de phase selon un second mode de réalisation;
• La Fig. 3C représente un module d'estimation de phase permettant de mettre en oeuvre une poursuite de phase selon un troisième mode de réalisation ;
• La Fig. 4 représente les performances du module d'estimation de phase la Fig. 3B;
• Les Figs. 5A-5C représentent les performances d'une méthode de poursuite de phase selon un mode de réalisation de l'invention, pour différentes valeurs d'offset de fréquence entre l'émetteur et le récepteur FBMC.
• Les Figs. 6A-6B illustrent les performances d'un récepteur FBMC utilisant une méthode de poursuite de phase selon un mode de réalisation de l'invention.

Other features and advantages of the invention will appear on reading preferred embodiments of the invention, with reference to the appended figures among which:

• The Fig. 1 represents a telecommunication system FBMC known from the state of the art;
• The Fig. 2 represents a FBMC receiver using a phase tracking method according to a general embodiment of the invention;
• The Fig. 3A represents a phase estimation module making it possible to implement a phase tracking according to a first embodiment of the invention;
• The Fig. 3B represents a phase estimation module making it possible to implement a phase tracking according to a second embodiment;
• The Fig. 3C represents a phase estimation module making it possible to implement a phase tracking according to a third embodiment;
• The Fig. 4 represents the performance of the phase estimation module Fig. 3B ;
• The Figs. 5A-5C represent the performance of a phase tracking method according to one embodiment of the invention, for different frequency offset values between the transmitter and the FBMC receiver.
• The Figs. 6A-6B illustrate the performance of a FBMC receiver using a phase tracking method according to an embodiment of the invention.

DETAILED PRESENTATION OF PARTICULAR EMBODIMENTS

We will consider in the following a FBMC receiver as described in the introductory part, this receiver can be implemented in the time domain or in the frequency domain, in a manner known per se. In the following, we will assume, in the absence of specific remarks, that the FBMC receiver is implemented in the time domain. Those skilled in the art will however understand that the phase tracking method is applicable regardless of the type of implementation.

The idea underlying the invention is to perform a phase estimation using symbols estimated in a simplified manner, the real and imaginary parts are expressed on a single bit.

More specifically, the Fig. 2 represents a FBMC receiver implementing a phase tracking method according to a general embodiment of the invention.

The FBMC receiver has a general structure similar to that described in relation to the Fig. 1 . More specifically, it comprises a baseband translation module 210, an analysis filter bank, 220, followed by an FFT module. The frequency components at the output of the FFT module are equalized in the frequency domain by means of an equalizer 235, in a manner known per se. In the case of an implementation of the FBMC receiver in the frequency domain, the analysis filtering and the equalization are performed after the FFT module. Of course, if the transmission channel is purely additive, the equalization is not necessary. The frequency components, where appropriate equalized, are considered after filtering by the analysis filters and the FFT, the order of operations depending on the type of implementation.

These frequency components are then delayed in a FIFO buffer 240 before being each multiplied by a phase correction factor in the multipliers 245 and undergo OQAM demodulation in the module 250. This demodulation is followed by a channel decoding (not shown). .

The FBMC receiver further comprises a phase estimator module, 260, using simplified symbols, as detailed below. This estimator makes an estimate of the phase shift between the frequency components and these simplified symbols. The estimated phase, φ, is used to calculate a phase correction factor exp (- jφ ). The phase correction factor is multiplied with each of the frequency components, delayed by the FIFO buffer 240. The delay corresponds to the processing time in the estimator. Advantageously, for reasons of timing, the delay is chosen equal to the calculation period of the FFT and the phase estimation is carried out at the same time.

The phase correction by the multipliers 245 is performed at each FFT block, that is to say at each FBMC symbol. This "instantaneous" phase correction is advantageously completed by an "average" phase correction. To do this, the estimated phases φ or the phase correction factors exp ( φ ) are averaged using a recursive filter (IIR filter) low-pass to provide a mean correction factor. The time constant of the low-pass filter can be chosen to be of the order of the duration of a packet. The average correction factor is then applied at the output of the FFT module (before or after the equalizer 235, when it is present) on all the frequency components thanks to the multipliers 233. Alternatively, the average correction factor can be applied at the output of the baseband translation module 210.

dans le module d'estimation 260. Dans ce cas, la poursuite de phase est alors hybride au sens où elle comprend une compensation de phase supervisée au début de chaque paquet (ou d'une pluralité de paquets) et de manière aveugle entre deux estimations supervisées consécutives.In addition to the blind phase estimation, the module 260 may periodically perform a phase estimation from pilot symbols, for example pilot symbols present in the preamble of the packets. This variant has been represented in the Fig. 2 by optional consideration of pilot symbols $d_{\mathrm{<figure-callout\; id="0"\; label="k\; P\; m"\; filenames="imgf0006.png,imgf0007.png"\; state="\{\{state\}\}">k\; </figure-callout>}}^P\left(m_{}\right)\left({}_0\right)$

in the estimation module 260. In this case, the phase tracking is then hybrid in that it includes supervised phase compensation at the beginning of each packet (or a plurality of packets) and blindly between two estimates. consecutive supervised.

The phase estimation module 260 can be made according to different variants described below.

The Fig. 3A represents a phase estimation module according to a first embodiment.

= (r̃_k [m]) de la composante alors que si la sous-porteuse porte une valeur imaginaire de symbole QAM (par exemple sous-porteuse d'indice impair), la donnée sera estimée comme la partie imaginaire de cette composante, d̂_k (m) =

(r̃_k [m]).This receives the frequency components of the received signal, after demodulation in baseband, filtering by the analysis filter bank and, where appropriate, equalization. These frequency components are denoted r _k [ m ] , k = 0, .., K - 1 where k is a subcarrier index. The module 330 determines, for each of these components, the data transmitted on the subcarrier. More precisely, if the subcarrier bears a real QAM symbol value (for example even-number subcarrier), the datum is estimated as the real part d _k ( m )

= ( r _k [ m ]) of the component whereas if the subcarrier bears an imaginary symbol value QAM (for example, subcarrier of odd index), the data will be estimated as the imaginary part of this component, d _k ( m ) =

( r _k [ m ]).

(r̃_k [m])) ou sgn(

(r̃_k [m])) et fournit un bit (symbole BPSK) en conséquence, à savoir -1 si le signe est négatif et +1 si le signe est positif.The estimated data by the module 330 is then coded on a bit. More precisely, the sign detector 340 detects the sign of the datum thus estimated, namely sgn (

( r _k [ m ])) or sgn (

( r _k [ m ])) and provides a bit (BPSK symbol) accordingly, ie -1 if the sign is negative and +1 if the sign is positive.

• si k est pair, $${\hat{s}}_k\left[m\right]=\mathrm{sgn}\left(\Re \left({\tilde{r}}_k\left[m\right]\right)\right)$$
  
• si k est impair, $${\hat{s}}_k\left[m\right]=j\mathrm{sgn}\left(\mathfrak{I}\left({\tilde{r}}_k\left[m\right]\right)\right)$$
  

The module 350 constructs a simplified symbol, noted ŝ _k [ m ] from the sign detected by the module 340. More precisely:

• if k is even, $${\hat{s}}_k\left[m\right]=\mathrm{sgn}\left(\Re \left({\tilde{r}}_k\left[m\right]\right)\right)$$
  
• if k is odd, $${\hat{s}}_k\left[m\right]=j\mathrm{sgn}\left(\mathfrak{I}\left({\tilde{r}}_k\left[m\right]\right)\right)$$
  

The simplified symbol ŝ _k [ m ] is simply a simplified estimate, reduced to the sign of the data carried by the subcarrier k. Therefore, the real part or the imaginary part of the simplified symbol is coded on a single bit. The term "simplified symbol" reflects the fact that the QAM symbol (for example 64-QAM) is encoded over several bits while the simplified symbol is encoded on only one bit (sign bit).

de la composante de la sous-porteuse k, r̃_k [m], avec le symbole simplifié obtenu pour cette même sous-porteuse, ŝ_k [m]. Les produits hermitiens ainsi obtenus pour les différentes porteuses sont ensuite fournis à un module de calcul qui détermine l'argument φ̂ de la somme de ces produits, c'est-à-dire : $$\hat{\phi }=\arg \left({\displaystyle \sum _{k=0}^{K-1}}{\tilde{r}}_k\left[m\right]{\hat{s}}_k^{*}\left[m\right]\right)$$

A multiplier 360 then performs the Hermitian product ${\tilde{r}}_k\left[m\right]{\hat{s}}_k^{*}\left[m\right]$

of the component of the subcarrier k, r _k [ m ], with the simplified symbol obtained for this same subcarrier, ŝ _k [ m ]. The Hermitian products thus obtained for the different carriers are then supplied to a calculation module which determines the argument φ of the sum of these products, that is to say: $$\hat{\phi }=\arg \left({\displaystyle \underset{k=0}{\overset{K-1}{\Sigma }}}{\tilde{r}}_k\left[m\right]{\hat{s}}_k^{*}\left[m\right]\right)$$

The Fig. 3B represents a phase estimation module according to a second embodiment.

As in the first embodiment, the phase estimation module receives the frequency components of the received signal, filtered by the analysis battery. If necessary, the frequency components, obtained at the output of FFT, are equalized as indicated above. Unlike the first embodiment, two simplified symbols are estimated by frequency component: a first simplified symbol corresponding to the data itself, carried by the sub-carrier and a second simplified symbol corresponding to the interference on the same sub-carrier - carrier, due to data on adjacent carriers and at the previous / next instants. The following table gives an example of interference generated by a data conventionally equal to 1, carried by the subcarrier k at time m. The impulse response of the prototype filter is here of length L = 2. m - 2 m - 1 m m + 1 m + 2 k - 1 -0.125 -0.206j 0239 0.206j -0.125 k 0 0564 1 0564 0 k + 1 -0.125 0.206j 0239 -0.206j -0.125

From a data value for a subcarrier and an instant ( k, m ) it is known to determine, from the coefficients of the synthesis filter, the interference generated on the adjacent subcarrier ( k - 1, k + 1) as well as for the previous instants ( m - 2, m - 1) and following ones ( m + 1, m + 2) .

The modules 331 first estimate the data on the different subcarriers. This estimate is identical to that made by the modules 330 in the first embodiment.

The modules 332 for their part estimate the interference generated on each sub-carrier. For a given subcarrier, the interference is determined from the estimated data for the adjacent subcarriers and, if appropriate for the previous instants.

In instant m and for a subcarrier k, the estimated datum is denoted d _k ( m ) and the estimated interference is denoted I _k ( m ) . For each subcarrier k, the two sign detectors 340 determine the respective signs of d _k ( m ) and _k ( m ) .

• si k est pair, $${\hat{s}}_k\left[m\right]=\mathrm{sgn}\left({\hat{d}}_k\left(m\right)\right)+j\mathrm{sgn}\left({\hat{i}}_k\left(m\right)\right)$$
  
• si k est impair, $${\hat{s}}_k\left[m\right]=\mathrm{sgn}\left({\hat{i}}_k\left(m\right)\right)+j\mathrm{sgn}\left({\hat{d}}_k\left(m\right)\right)$$
  

For each sub-carrier, the module 350 constructs a simplified symbol, denoted by des _k [ m ], from the signs detected by the modules 340. More precisely:

• if k is even, $${\hat{s}}_k\left[m\right]=\mathrm{sgn}\left({\hat{d}}_k\left(m\right)\right)+j\mathrm{sgn}\left({\hat{i}}_k\left(m\right)\right)$$
  
• if k is odd, $${\hat{s}}_k\left[m\right]=\mathrm{sgn}\left({\hat{i}}_k\left(m\right)\right)+j\mathrm{sgn}\left({\hat{d}}_k\left(m\right)\right)$$
  

It can thus be seen that the real part and the imaginary part of the simplified symbol are each coded on a single bit.

de la composante de la sous-porteuse k, r̃_k [m], avec le symbole simplifié obtenu pour cette même sous-porteuse, ŝ_k [m]. Les produits hermitiens obtenus pour les différentes porteuses sont ensuite fournis à un module de calcul, 370, qui détermine comme précédemment l'argument φ̂ par : $$\hat{\phi }=\arg \left({\displaystyle \sum _{k=0}^{K-1}}{\tilde{r}}_k\left[m\right]{\hat{s}}_k^{*}\left[m\right]\right)$$

A multiplier 360 then performs the Hermitian product ${\tilde{r}}_k\left[m\right]{\hat{s}}_k^{*}\left[m\right]$

of the component of the subcarrier k, r _k [ m ], with the simplified symbol obtained for this same subcarrier, ŝ _k [ m ]. The Hermitian products obtained for the different carriers are then supplied to a calculation module, 370, which determines as previously the argument φ by: $$\hat{\phi }=\arg \left({\displaystyle \underset{k=0}{\overset{K-1}{\Sigma }}}{\tilde{r}}_k\left[m\right]{\hat{s}}_k^{*}\left[m\right]\right)$$

The Fig. 3C represents a phase estimation module according to a third embodiment.

This embodiment differs from the previous one by the presence of the regeneration module 320. This module comprises an OQAM demodulator (identical to the OQAM demodulator, 180, the Fig. 1 ), a channel decoder (implementing for example the Viterbi algorithm), followed by a channel coder an OQAM modulator (identical to the OQAM modulator, 110, of the Fig. 1 ). This results in output of the module 320 frequency components regenerated from the data corrected by the channel decoding. The simplified symbols are constructed from these regenerated frequency components r ₀ [ n ], ..., r _{K -1} [ n ] instead of the original frequency components, r ₀ [ n ], ..., r _{K -1} [ n ].

According to a fourth embodiment not shown of the phase estimation module, the regeneration module 320 may be alternatively provided upstream of the modules 330 of the Fig. 3A . In this case, the data of the different sub-carriers are estimated from the regenerated frequency components r ₀ [ n ], ..., r _{K -1} [ n ] instead of the original frequency components, r ₀ [ n ] , ..., r _{K -1} [ n ], and the simplified symbols are constructed from the data thus estimated, as explained in relation to the Fig. 3A .

The Fig. 4 illustrates the performance of the phase estimator used by the blind phase tracking module of the Fig. 3B .

More precisely, this figure represents the probability density of the phase estimation error in radians of different estimators, for a signal-to-noise ratio of 13 dB. Curve 410 gives the probability density of the estimation error, for an ideal phase estimator, assuming a perfect reconstruction of the interference (estimator called "genius" estimating without error the term of interference I _k ( n , φ) of equation (5)). Curve 430 represents the probability density of the estimation error for a phase estimator of the state of the art, using a partial estimation of each symbol, as proposed in the aforementioned P. Amini article.

Finally, the curve 420 gives the probability density of the phase estimation error for the estimator of the Fig. 3B that is, using simplified symbols representing the signs of data and interference.

It will be noted that the phase estimator of the Fig. 3B is significantly better than that of the prior art for less complexity.

We have shown in Figs. 5A-5C symbol error rate curves as a function of the signal-to-noise ratio, for different phase tracking methods in a FBMC receiver. Frequency offsets between transmitter and receiver are respectively 0Hz for the Fig. 5A , 40 Hz for the Fig. 5B and 200Hz for the Fig. 5C .

For the sake of comparison, there is furthermore shown in each figure the case where the receiver was perfectly synchronized with the transmitter (zero frequency offset, curve 510).

Conversely, there is shown in 550 the case where no phase tracking was performed.

The curve 520 corresponds to a phase tracking according to the method of the prior art based on a partial estimation of the symbols.

Curve 530 corresponds to a phase tracking using the phase estimator of the Fig. 3B .

Finally, the curve 540 corresponds to an ideal phase tracking for which it is assumed that the phase estimator is of the "engineering" type (perfect knowledge of the term of interference).

Note that, in all cases, the phase tracking method according to the invention leads to a lower symbol error rate than in the prior art, especially since the signal-to-noise ratio is degraded. .

The Figs. 6A and 6B represent the performance of a FBMC receiver using a phase tracking method according to an embodiment of the invention.

The performances are here related to a complete reception chain including synchronization, channel estimation, phase tracking and channel decoding. They are therefore expressed in bit error rate as a function of the signal-to-noise ratio.

The Figs. 6A and 6B are respectively relative to QPSK modulation and 64-QAM modulation. In other words, the symbols carried by the sub-carriers belong to a QPSK modulation alphabet in the first case and 64-QAM in the second case.

In the Fig. 6A curve 610 corresponds to the case where there is no frequency offset between the transmitter and the receiver and where the phase estimation is performed on the only pilot symbols of the preamble. In other words, the phase estimation is supervised and no phase tracking is performed on the payload portion of the packet.

Curve 620 corresponds to the same case as curve 610, with the difference that phase tracking is performed on the payload after estimating the phase shift (supervised) on the preamble. In this sense, the curve 620 relates to a hybrid tracking method as defined in the introductory part. The phase tracking on the useful part is carried out using the phase estimation module of the Fig. 3B .

The curves 630 and 640 relate to the same phase tracking strategies as the curves 610 and 620 but for a frequency offset of 50 Hz between the receiver and the transmitter.

Note that the blind pursuit on the useful part of the package, according to the present invention, substantially reduces the error rate compared to a simple supervised method.

The Fig. 6B represents the performance of a full FBMC reception chain for 64-QAM modulation and no frequency offset between the receiver and the transmitter. The curve 650 is relative to the ideal case where an exact estimate of the interference (engineering estimator) is available, the curve 660 in the case where a phase estimation is carried out on the single preamble (supervised phase estimation ), without phase tracking on the payload portion of the packet. Finally, the curve 670 is relative to the case where the phase is estimated on the preamble but where a phase continuation is then carried out on the useful part of the packet by means of the phase estimation module of the Fig. 3B .

We notice again in Fig. 6B that the phase tracking method based on simplified symbols, as proposed in the present invention, makes it possible to obtain performances very close to the ideal case for a relatively low algorithmic complexity.

Claims (7)

1. Blind phase tracking method for FBMC receiver, whereby the received signal is demodulated into baseband, filtered by an analysis filter bank and subjected to FFT, in order to provide a plurality of frequency components, whereby each frequency component corresponds to a sub-carrier, in which:

   - one estimates (330, 331) the data transmitted on each subcarrier from the said frequency components;

   - one determines (340) the sign of the data thus estimated;

   - one estimates 30,332) from the data thus estimated the interference affecting each of the subcarriers;

   - one determines (340) the sign of each interference thus estimated;

   - one constructs a simplified symbol (350) for each subcarrier from the sign of the estimated data for this subcarrier and the sign of the estimated interference for this subcarrier, whereby the real and the imaginary part of the simplified symbol is each encoded in a single bit;

   - one estimates a phase difference (370) between the frequency components and the said simplified symbols;

   - one applies a phase correction (233, 245) to the frequency components from the phase difference thus estimated.
2. Phase tracking method according to claim 1, characterised in that the estimation of the data of the subcarriers and/or interference affecting each of the subcarriers is effected from previously regenerated frequency components, whereby the regenerated frequency components are obtained (320) from frequency components by means of processing comprising OQAM demodulation and channel decoding followed by a new OQAM modulation.
3. Phase tracking method according to claim 1, characterised in that the frequency components are subject to equalisation before the estimation of the data and/or interference on each of the subcarriers.
4. Phase tracking method according to any of the precedent claims, characterised in that the said phase shift is estimated by averaging over all subcarriers of the Hermitian products of the frequency components with the simplified symbols.
5. Phase tracking method according to any of the precedent claims, characterised in that the phase shift thus estimated is filtered using a low pass filter, whereby a mean phase correction factor is obtained from the phase shift thus filtered, while the mean phase correction factor is applied (233) to the received signal, after translation to baseband.
6. Phase tracking method according to any of claims 1 to 4, characterised in that the phase shift thus estimated is filtered using a low pass filter, whereby a mean phase correction factor is obtained from the phase shift thus filtered, while the average phase correction factor is applied (233) to the said frequency components.
7. Phase tracking method according to any of the preceding claims, characterised in that the received signal is in the form of packets, whereby each packet comprises a preamble and a payload, and whereby the said phase difference is estimated first in a first step from pilot symbols belonging to the preamble and then, in a second step, by means of the said blind phase tracking from the signal during the payload.

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